In how many ways 4 rings of different types can be worn in 3 fingers ?

Options

A. a. 49
B. b. 12
C. c. 24
D. d. 81

Answer

To solve the problem of how many ways 4 rings of different types can be worn on 3 fingers, we can break the solution down into several steps:

### Step 1: Choose 3 Rings from 4
Since we have 4 different rings and we can only wear 3 at a time, we first need to choose which 3 rings we will wear. This can be calculated using combinations.

\[ \text{Number of ways to choose 3 rings from 4} = \binom{4}{3} = 4 \]

### Step 2: Distribute the 3 Rings to 3 Fingers
Once we have chosen 3 rings, we need to distribute these rings across the 3 fingers. Each of the 3 rings can go on any of the 3 fingers. Therefore, for each ring, we have 3 choices.

\[ \text{Number of ways to distribute 3 rings to 3 fingers} = 3^3 = 27 \]

### Step 3: Arrange the 3 Rings
The 3 rings can be arranged among themselves in different orders. The number of arrangements of 3 rings is given by the factorial of the number of rings.

\[ \text{Number of arrangements of 3 rings} = 3! = 6 \]

### Step 4: Calculate the Total Ways
Now, we can combine all these calculations to find the total number of ways to wear the rings.

\[ \text{Total ways} = \text{Ways to choose rings} \times \text{Ways to distribute} \times \text{Ways to arrange} \]

Substituting the values we calculated:

\[ \text{Total ways} = 4 \times 27 \times 6 \]

Calculating this gives us:

\[ 4 \times 27 = 108 \]
\[ 108 \times 6 = 648 \]

Thus, the total number of ways to wear 4 rings of different types on 3 fingers is **648**.

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